Problem: Simplify the following expression: $z = \dfrac{r}{10} - \dfrac{r}{8}$
Explanation: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $10$ and $8$ $\lcm(10, 8) = 40$ $ z = \dfrac{4}{4} \cdot \dfrac{r}{10} - \dfrac{5}{5} \cdot \dfrac{r}{8} $ $z = \dfrac{4r}{40} - \dfrac{5r}{40}$ $z = \dfrac{4r -5r}{40}$ $z = \dfrac{-r}{40}$